The optimal edge for containing the spreading of SIS model

Abstract

Numerous real-world systems, for instance, communication platforms and transportation systems, can be abstracted into complex networks. Containing spreading dynamics (e.g. epidemic transmission and misinformation propagation) in networked systems is a hot topic on multiple fronts. Most of the previous strategies are based on the immunization of nodes. However, sometimes, these node-based strategies can be impractical. For instance, in train transportation networks, it is excessive to isolate train stations for flu prevention. On the contrary, temporarily suspending some connections between stations is more acceptable. Thus, we pay attention to the edge-based containment strategy. In this study, we develop a theoretical framework to find the optimal edge for containing the spread of the susceptible-infected-susceptible model on complex networks. To be specific, by performing a perturbation method to the discrete-Markovian-chain equations of the SIS model, we derive a formula that approximately provides the decremental outbreak size after the deactivation of a certain edge in the network. Then, we determine the optimal edge by simply choosing the one with the largest decremental outbreak size. Note that our proposed theoretical framework incorporates the information of both network structure and spreading dynamics. Finally, we test the performance of our method by extensive numerical simulations. Results demonstrate that our strategy always outperforms other strategies that are based only on structural properties (degree or edge betweenness centrality). The theoretical framework in this study can be extended to other spreading models and offers inspiration for further investigations on edge-based immunization strategies.